I am trying to generate code for plotting anti fractals and getting error

Question

Akansha 2024-10-26

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2162285-i-am-trying-to-generate-code-for-plotting-anti-fractals-and-getting-error

回答： Voss 2024-10-30

i am taling k=2 in this function Q_c(z) ,thetha=0.2 ,A = [−6, 4.7] × [−5.5, 5.5] tri-corn generated in PMO .i am getting error in my code.

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Akansha 2024-10-27

编辑：Voss 2024-10-27

在 MATLAB Online 中打开

i need this output. i am not getting correct output by this code and Q_c{z)=z^2+c

%Constants

dr = 800; % Increased resolution of the grid

xmin = -6; xmax = 4.7; % Real range

ymin = -5.5; ymax = 5.5; % Imaginary range

K = 200; % Increased maximum number of iterations

theta = 0.2; % Parameter theta

k = 2; % Parameter k

M = 256; % Number of colors in the colormap

% Create a grid of complex numbers over A

re = linspace(xmin, xmax, dr); % Real part

im = linspace(ymin, ymax, dr); % Imaginary part

c_grid = re + im' * 1i; % Complex grid A = [-6, 4.7] x [-5.5, 5.5]

% Initialize escape time matrix

E = zeros(size(c_grid)); % Escape time matrix

% Pre-calculate fixed R based on theta and k

R_base = (2 * theta)^(1 / (k - 1));

% Loop over each point in the grid A

for a = 1:dr

for b = 1:dr

c = c_grid(a, b); % Current point in A

R = max(abs(c), R_base); % Calculate R for this c

z = 0; % Initial z0

n = 0; % Iteration counter

% Iterate using the Tricorn function

while n <= K

u_n = (1 - theta) * z + theta * (conj(z)^2 + c); % Compute u_n

z_next = conj(u_n)^2 + c; % Compute z_{n+1}

% Check for escape condition

if abs(z_next) > R

break;

end

z = z_next; % Update z

n = n + 1; % Increment iteration counter

end

% Map n to a color index

E(a, b) = floor((M - 1) * n / K); % Store escape time

end

% Plotting the fractal

figure; % Create a new figure

imagesc(re, im, E); % Display the escape time matrix

colormap(jet(M)); % Use 'jet' colormap (replace with 'parula', 'hot', etc. if desired)

axis xy; % Correct the axis orientation

set(gca, 'YDir', 'normal'); % Ensure imaginary axis direction is correct

colorbar; % Add a colorbar

title('Anti-Fractal (Tricorn) with PMO Method');%"

xlabel('Real axis');

ylabel('Imaginary axis');

axis([xmin xmax ymin ymax]); % Set axis limits explicitly

Akansha 2024-10-28

Akansha 2024-10-28

this output i need but not getting

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Answer 1

Voss 2024-10-30

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2162285-i-am-trying-to-generate-code-for-plotting-anti-fractals-and-getting-error#answer_1539490

在 MATLAB Online 中打开

Generation_of_Antifractals_via_Hybrid_Picard-Mann_.pdf

Picking z0=c instead of z0=0, correcting the definition of R_base to have 2/theta instead of 2*theta, decreasing the max number of iterations so you can see some color variation, and choosing a similar colormap, gets you closer to the reference image:

%Constants

cmap = [234 55 36; 234 84 40; 238 124 50; 243 178 62; 244 193 67; 246 235 78; 221 250 82; 112 238 113; 40 59 126; 0 0 0]/255;

M = size(cmap,1); % Number of colors in the colormap

dr = 800; % Increased resolution of the grid

xmin = -6; xmax = 4.7; % Real range

ymin = -5.5; ymax = 5.5; % Imaginary range

K = M-1; % maximum number of iterations

theta = 0.2; % Parameter theta

k = 2; % Parameter k

% Create a grid of complex numbers over A

re = linspace(xmin, xmax, dr); % Real part

im = linspace(ymin, ymax, dr); % Imaginary part

c_grid = re + im.' * 1i; % Complex grid A = [-6, 4.7] x [-5.5, 5.5]

% Initialize escape time matrix

E = zeros(size(c_grid)); % Escape time matrix

% Pre-calculate fixed R based on theta and k

R_base = (2 / theta)^(1 / (k - 1));

% Loop over each point in the grid A

for a = 1:dr

for b = 1:dr

c = c_grid(a, b); % Current point in A

R = max(abs(c), R_base); % Calculate R for this c

z = c; % Initial z0

n = 0; % Iteration counter

% Iterate using the Tricorn function

while n <= K

u_n = (1 - theta) * z + theta * (conj(z)^k + c); % Compute u_n

z_next = conj(u_n)^k + c; % Compute z_{n+1}

% Check for escape condition

if abs(z_next) > R

break;

end

z = z_next; % Update z

n = n + 1; % Increment iteration counter

end

% Map n to a color index

E(a, b) = n;

end

% Plotting the fractal

figure; % Create a new figure

imagesc(re, im, E); % Display the escape time matrix

colormap(cmap); % Use 'jet' colormap (replace with 'parula', 'hot', etc. if desired)

axis xy; % Correct the axis orientation

set(gca, 'YDir', 'normal'); % Ensure imaginary axis direction is correct

colorbar; % Add a colorbar

title('Anti-Fractal (Tricorn) with PMO Method');

xlabel('Real axis');

ylabel('Imaginary axis');

axis([xmin xmax ymin ymax]); % Set axis limits explicitly

The pseudo-code snippet you posted (Algorithm 2) is for Anti-Julia set, but the reference image you posted is a tricorn, which is based on Algorithm 1, as defined in the attached pdf (downloaded from here).

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I am trying to generate code for plotting anti fractals and getting error

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